A new start for local composite operators

TL;DR

This paper introduces a formalism for local composite operators, demonstrating its effectiveness in ensuring renormalizability and gauge independence in specific quantum field theories up to several loops.

Contribution

The paper develops a novel formalism for local composite operators, ensuring a unique, multiplicatively renormalizable effective potential expressed as a sum of 1PI diagrams.

Findings

Renormalizability confirmed up to three loops in $lambda \u03a6^4$ theory.

Gauge independence of the effective potential verified up to two loops in the Coleman-Weinberg model.

Effective potential can be interpreted as an energy-density.

Abstract

We present a formalism for local composite operators. The corresponding effective potential is unique, multiplicatively renormalizable, it is the sum of 1PI diagrams and can be interpreted as an energy-density. First we apply this method to $\lambda \Phi^4$ theory where we check renormalizability up to three loops and secondly to the Coleman-Weinberg model where the gauge independence of the effective potential for the local composite operator $\phi\phi^*$ is explicitely checked up to two loops.